MathDB

We have a

2\times n

rectangle. We call each

1\times1

square a room and we show the room in the

i^{th}

row and

j^{th}

column as

(i,j)

. There are some coins in some rooms of the rectangle. If there exist more than

1

coin in each room, we can delete

2

coins from it and add

1

coin to its right adjacent room OR we can delete

2

coins from it and add

1

coin to its up adjacent room. Prove that there exists a finite configuration of allowable operations such that we can put a coin in the room

(1,n)

Problem Statement